Direct current double integrator



March 14, 1961 s. F. EYESTONE 2,974,868

DIRECT CURRENT DOUBLE INTEGRATOR Filed Nov. 1, 1948 4 Sheets-Sheet 1 226 27 L ,6 Up [5 CURRENT 7'0 BE INTEGRATED I Q 6 Q 5 F 1 I a 7/ l FIG.

S. F. EYESTONE IN VEN TOR.

A T TORNE Y March 1961 s. F. EYESTONE 2,974,868

DIRECT CURRENT DOUBLE INTEGRATOR Filed Nov. 1, 1948 4 Sheets-Sheet 2 5. F. E YE 5' TONE IN VEN TOR.

March 14, 1961 s. F. EYESTONE 2,974,868

DIRECT CURRENT DOUBLE INTEGRATOR Filed NOV. 1, 1948 4 Sheets-Sheet 3 5. F. E YE STONE INVENTOR.

A T TORNE Y March 14, 1961 s. F. EYESTONE 2,974,368

DIRECT CURRENT DOUBLE INTEGRATOR Filed Nov. 1, 1948 4 Sheets-Sheet 4 A. 0. 5 OURGE 5 GURREN 0 BE i INTEGRA D 20 2/ 5. F: EYE STONE 8 INVENTOR.

Arrok/vs iinitedl States Patent Shirley F. Eyestone, Inglewood, Calif., assignor to North American Aviation, Inc.

Filed Nov. 1, 1948, Ser. No. 57,815

13 Claims. (Cl. 235-183) This invention pertains to the performance of mathematical operations by the usev of a number of rotating masses. It more particularly relates to the electromechanical double integration of an electric current such as that in an electromagnetically restrained mass accelerometer.

An object of this invention is to provide a method of performing multiple integration and differentiation by electromechanical means.

Another object of this invention is to provide a system of rotating masses and driving means for the purpose of computing multiple integrals and differentials of time functions.

Other objects of invention will become apparent from the following description taken with the accompanying drawings, wherein Fig. l is a perspective view, partly in section, of a simplified form of the invention;

Fig. 2 is a plan view of another embodiment of the invention;

Fig. 3 is an elevational arrangement of Fig. 2;

Fig. 4 isa cross-section taken at'4-4 in Fig. 3;

Fig. 5 is a view, partly in section, taken generally at 55 in Fig. 3;

Fig. 6 is a partial cross-section taken at 6-6 in Fig. 3;

Fig. 7 is an enlarged cross-section taken at 7-7 in Fig. 3; and

Fig. 8 is a wiring diagram of the arrangement of the invention shown in Fig. 2.

Referring to Fig. 1 the invention consists essentially of three coaxially associated rigid masses, 1, 2, and 3. Mass 1 serves as a rigid frame, a means for mounting the device, and as a support for mass 2, tachometer generator 4, motor 5, revolution counter 6, and servo amplifier 7. Mass 2 supports coils 8 and the outer elements 9 and it) of position pickofi' 11, and is free to rotate with respect to mass 1.

Mass 3 comprises a ferromagnetic frame 12 free to rotate about the axis of rotation of mass 2 and serves as a support for a permanent magnet 13 and the movable element 14 of position picko-ff 11.

As stated above, one of the objects of this invention is to perform the operations of single and multiple integration and differentiation. When a torque is applied to a mass free to rotate, such as mass 2, the mass accelerates according to Newtons second law of motion in such a manner that the acceleration is directly proportional to the torque, and inversely proportional to the rotational inertia characteristics of the mass. Since the inertial characteristic of any particular mass is a constant for all accelerations, the acceleration is always proportional to the torque as applied by motor 5. Further, acceleration is, by definition, the first differential of velocity, and the second differential of displacement. Conversely, velocity is the first integral of acceleration, and displacement is the second integral of acceleration. Therefore, the velocity of a mass rotating under the influence of a torque view, partly in section, of the ice is a measure of the first integral of the torque, and the displacement of a mass rotating under the influence of a torque is a measure of the second integral of the torque.

In this invention, the function to be integrated is supplied electrically from, for example, computer means (not shown) or electromagnetic accelerometers whose output is a current which is proportional to a linear acceleration, as a signal in terms of a current which varies with time according to the function to be integrated. This signal is applied through slip rings 15 and 16 or other suitable low-friction conducting means to coils 8 in Fig. 1. A magnetic field is formed in air gap 25 by means of permanent magnet 13, and a return path is furnished by frame 12 constructed of ferromagnetic material. Coils 8 are attached to mass 2 and are arranged so that they pass through air gap 25 with the result that the passage of current through these coils causes a proportional torque to be exerted on masses 2 and 3 in an opposite sense, causing them to take on an angular acceleration of magnitude proportional to the current. The relative angular displacement between masses 2 and 3 resulting from these accelerations is detected by relative position pickoff 11, which generates an electrical signal by means of a capacitance bridge, proportional to said displacement. An example of a suitable capacitance bridge is shown in Pig. 3 of Patent No. 2,319,940 issued September 12, 1939 to W. A. Marrison for Gravitational Force Measuring Apparatus. Plate 14 of Fig. 1 corresponds to plate b in the patent to Marrison, while plates 9 and 10 of Fig. 1 correspond to plates a and c of the patent to Marrison. Plates d, e, and f of the patent to Marrison form the other legs of a capacitance bridge and are fixed in the device of this invention. When plate 14 moves, the bridge becomes unbalanced and generates a signal proportional to the movement of plate 14. Capacitance bridges are well-known in the art. Other examples of suitable circuits for use with capacitive pick-ofll 11 are those shown in Fig. 5 of patent application Serial No. 57,686 filed November 1, 1948, now Patent No. 2,882,034, in the name of John M. Wuerth, for Accelerometer and Integrator, and patent application Serial No. 57,816 filed November 1, 1948 in the name of Shirley F. Eyestone and Wesley E. Dickinson, for Accelerometer. The resulting signal is fed through slip rings 26 and 27 to the remaining parts of the capacitance bridge and amplifier '7 and is amplified and used to control motor 5 in such a manner that it introduces a rotation to mass 2 in the proper sense to cause a new rotation for the pickoif element 14 to be sought. The torque acting between masses 2 and 3 is proportional to the current to be integrated. The motor torque acts between masses 1 and 2 in response to the pickoif rotation, causing mass 2 to accelerate in the same direction as the pickoif rotation. A new rotation of the pickoif is thereby caused and a modified torque supplied by the motor. Mass 2 thus tends to catch up with mass 3, and the motor torque necessary to produce this result is proportional to the current to be integrated. Therefore, the first and second time integrals, respectively, of the current to be integrated are obtained by measurement of the angular velocity and displacement of mass 2. The overall result of this arrangement is that masses 2 and 3 experience an angular acceleration which is proportional to the current introduced to coils 8 and rotate together with only sulficient relative displacement between them to produce the necessary signal to control motor 5. Because motor 5 is connected to mass 2, it rotates with mass 2. Thus, if the first integral of the signal to be integrated is not zero, both mass 2 and motor 5 rotate in proportion to the first integral Revolution counter 6 detects the total angular rotation of mass 2 and thus measures the second integral of the function to be integrated. The first integral is obtained by measurement of the angular velocity of mass 2, such velocity being measured by any suitable means such as tachometer 4 arranged to indicate the instanetaneous angular velocity of mass 2.

Referring now to Figs. 2, 3, 4, 5, 6, and 7, there is illustrated another embodiment of the device shown generally in Fig. 1. Mass 1a comprises a substantially cylindrical outer casing with an axial air entrance port 17. Mass 1a also serves as the stator of a motor described below in connection with mass 2a.

Mass 2a is a rigid shell supported in bearings 18 and 19 by mass In. Mass 2a carries two sets ofv coils 20' and 21 with functions similar to coils 8 and pickoff 11 in Fig. 1. functioning as motor in Fig. 1. Fig. 6 shows the rotor and stator slots in masses 1a and 2a. Several slip rings are provided at 22 for transmitting electrical energy from mass In to mass 2a.

Mass 3a comprises a permanent magnet 23 supported on air bearings 24 fed by air from port 17 and ducts 30, mass 3a thus having freedom for rotative movement about the axis of rotation of mass 2a. Fig. 7 shows the air hearings in detailed cross-section. Permanent magnet 23 is so shaped as to form, together with pole face 23a of lamination stack 3b, annular shaped air gaps 25 accommodating coils and 21. The relationship of coils 20 and 21 to air gaps is shown in Figs. 3, 4, and 5. Lamination stack 3b is fastened to .mass 3a by means of bracket 31 and turns therewith. j The embodiment of the invention shown in Figs. 2, 3, 4, 5, 6, and 7 differs in operation from that of Fig. 1 principally because the parts are arranged and utilized more efficiently. In this second embodiment the showing in Fig. 1 is modified by making motor 5 integral with masses 1 and 2. Coils 2t) and 21 perform all the functions of coils 8 and pickoff 11. Coils 20 are excited by an external alternating current source (no-t shown) through the slip rings at 22. These coils thus create a. constant strength alternating magnetic field in which mass 311 and lamination stack 3b constitute the magnet.

The current to be integrated is communicated to coils 21 through the slip rings and causes an angular deflection of mass 3a and elements 3b and 31 with respect to mass 2a by interaction with permanent magnet 23. This defiection causes an angular shift in the alternating current field, thus inducing an alternating current in coils 21 proportional in magnitude to the said deflection. As shown in the circuit diagram of Fig. 8, this alternating current is amplified in amplifier 7, which is sharply tuned to amplify only the frequency corresponding to the frequency of the alternating current and, hence, does not respond to the current to be integrated. The current to be integrated is thus, in effect, filtered out of the amplifier and, hence is prevented from afiecting the motor. The alternating current is then directed from the amplifier to the motor, which exerts a torque on mass 2a proportional to said current and in the direction of the above-mentioned amgular displacement of mass So from mass2a.

I As shown in Figs. 4 and 5, the air gap 25 between mass 3a and element 3b is long in comparison to its width and in comparison to the dimensions of coils 21. The nosignal position of mass 3a with respect to mass 2a is such that the coils 21 lie in the centers of their respective air gaps, thus being in a magnetically null position. Consequently, for small angular deflection, the deflection of mass 3a with respect tomass 2a does not result in an appreciable change of magnetic field relative to the coils and, hence, the proportionality ratio between torque and the current in coils 21 is not materially affected. 7

This air gap arrangement forms an important part of the invention because without it the required linearity between input signal and motor torque could not be obtained. The input signal being proportional to the torque applied to mass 2a by the motor windings, the first integral of the input signal is measured by the angular velocity of Mass 2a also serves as the rotor of a motor When this device is used as a ditferentiator, the function to be differentiated is one in terms of an angular velocity varying with time. Since the second derivative of angular displacement with respect to time is proportional to torque, and since the first derivative of angular velocity is equal to the second derivative of angular displacement, the torque necessary to produce a given angular velocity is proportional to the first derivative of such angular velocity, and the torque necessary to produce a given angular displacement is proportional to the second derivative of the angular displacement.

Therefore, in this invention the angular velocity or displacement to be differentiated is' applied by independent means to mass 2, in Fig. 1, and the relative position pickofif 11 and amplifier 7 are used to control the current in coils 3 so that a null condition of the relative motion between masses 2 and 3 is sought. Then the torque is measured by the current in coils 8. This current is proportional to, and therefore a measure of the first differential of the velocity and the second differential of the angular displacement of mass 2.

Although the invention has been described and illustrated in detail, it is to be clearly understood that the same is by way of illustration and example only and is not to be taken by way of limitation, the spirit and scope of this invention being limited only by the terms of the appended claims.

I claim:

1. Computing means comprising a reference frame, a

first and second mass independently rotatable about a common axis on said reference frame, means for producing a differential torque between said masses which is proportional to any-function to be integrated, means for applyingto said second mass a torque 'suflicient to cause said second mass to remain angularly undisplaced from said first mass, means for measuring the angular velocity and displacement of said two masses with respect to said reference frame tothereby measure the first and second integrals, respectively, of the function to be intc grated.

2. A device as recited in claim 1 in which said means for applying to said second mass a torque comprises a means for producing an electrical signal proportional to the displacement between said masses, means for amplifying said signal, and means for applying said sign-a1 to a motor drivably associated with said second mass.

3. A device as recited in claim 1 in which said means for producing said differential torque between said masses comprises coils attached to one of said masses movably disposed in magnetic air gaps attached to the other of said masses, and means for introducing a current into said coils so that when current flows in said coils a torque is produced displacing one mass angularly from the other in an amount proportional to said current.

4. Computing means comprising a rotor, an inertial means, means coaxially associated with said inertial means for constraining the same to move with said rotor, and means for generating an electrical signal proportional to the angular displacement between said rotor and said inertial means to thereby produce a signal which is proportional to the first derivative of the rotor velocity and the second derivative of the rotor displacement.

5. Computing means comprising a mass, means for rotating said mass, means for measuring the angular velocity and angular displacement of said mass, a second mass coaxially associated with said rotatable mass, means for angularly displacing said two masses with respect to each other by an amount proportional to some function of time to be integrated, means for producing an electric current proportional to said displacement, and means for amplifying said current and applying the same to said means for rotating said mass whereby said measured angular velocity and angular displacement are the first and second integrals, respectively, of the said function to be integrated.

6. A device as recited in claim 5 in which said means for angularly displacing said masses comprises permanent magnetic air gaps on said second mass containing movable electromagnetic coils attached to said first mass and in which said means for producing said electric current proportional to said displacement comprises said movable electromagnetic coils moving in said air gaps on which an alternating electromagnetic field has been superimposed by a second set of coils excited by alternating current but orthogonally disposed with respect to said movable coils.

7. A computing device comprising two relatively rotatable masses, means for rotating said masses, means for applying a differential torque between said masses in response to a variable signal the integral of which is to be computed, means for varying the relative displacement of said masses in response to said signal variations, means responsive to said variations in displacement for tending to maintain synchronous rotation of said masses, means for measuring the velocity and angular displacement of one of said masses, the measured angular velocity being the first integral of the signal value, and the measured displacement being the second integral of the signal value.

8. A device as recited in claim 7 in which said means responsive to said variations in displacement comprises a relative position pickoff and an amplifier operatively associated to drive said means for rotating said masses.

9. A computing device comprising two relatively rotatable masses, electric means for rotating said masses in response to a variable electric signal the integral of which is to be determined, magnet means operatively associated with said two masses for tending to displace said masses with respect to each other in response to said sign-a1 variations, means for detecting the relative positions of said masses, said rotating means being responsive to said position detecting means, whereby the measured angular velocity and displacement of one of said masses are respectively the first and second integrals of the signal value.

10. Computing means comprising two masses, means for producing between said masses a torque proportional to some function to be integrated, means for measuring the resultant relative angular velocity and angular displacement of said masses to thereby measure the first and second integrals respectively of the function to be integrated.

11. Computing means comprising two masses, means for applying to the first of said two masses an angular velocity which varies with time according to some function to be differentiated, means for applying a torque to the second of said two masses so as to cause it to predeterminately follow 'said first mass, and means for measuring said torque to thereby measure the first derivative of said function to be differentiated.-

12. Computing means comprising two masses, means for applying to the first of said two masses an angular displacement which varies with time according to some function to be differentiated, means for app-lying a torque to the second of said two masses so as to cause it to predeterminately follow said first mass, and means for measuring said torque to thereby measure the second derivative of said function to be differentiated.

:13. Computing means comprising a mass, means for rotating said mass, means for measuring the angular velocity and angular displacement of said mass, a second mass coaxially associated with said rotatable mass, permanent magnetic air gaps on said second mass, movable electromagnetic coils attached to said first mass, said electromagnetic coils being positioned in said air gap, an alternating-current source, aset of alternating-current coils connected to said alternating-current source orthogonally disposed with respect to said movable coils for superimposing an alternating electromagnetic field in said air gaps, means for amplifying the current in said movable coils and applying the same to said means for rotating said mass whereby said current produced in said movable coils is proportional to the angular displacement between said masses, and said measured angular velocity and angular displacement are the first and second integrals, respectively, of the said function to be integrated.

References Cited in the file of this patent UNITED STATES PATENTS 1,977,498 Staegemann Oct. 16, 1934 2,109,283 Boykow Feb. 22, 1938 2,185,767 Jefferies Jan. 2, 1940 2,266,449 Ullrich et a1. Dec. 16, 1941 2,414,108 Knowles et al. Jan. 14, 1947 2,444,329 Booth June 29, 1948 OTHER REFERENCES An All Electric Integrator, by R. N. Varney, published in Review of Scientific Instruments, volume 12, January 1942, PPS. 10-16. 

